UNOBSERVED COMPONENT TIME-SERIES MODELS WITH ARCH DISTURBANCES

This paper considers how ARCH effects may be handled in time series models formulated in terms of unobserved components. A general model is formulated, but this includes as special cases a random walk plus noise model with both disturbances subject to ARCH effects, an ARCH-M model with a time-varying parameter, and a latent factor model with ARCH effects in the factors. Although the model is not conditionally Gaussian, an approximate filter can be obtained and used as the basis for estimation. The performance of this method is examined on real data sets and Monte Carlo experiments are carried out. The method is extended to handle GARCH and a latent factor model based on the t-distribution.